We consider incomplete data problems in two different complex data contexts: group testing data and functional data. In the group testing data context, we consider estimating the conditional prevalence of a disease from ...

At any one time, more than 160 million children worldwide are infected with skin sores. In remote Aboriginal Australian communities, prevalence is as high as 40%. Skin sores infected with Group A Streptococcus (GAS) can ...

In this thesis, we use extreme value theory to fit statistical models to observations of Australian daily rainfall extremes. We build upon the existing literature by challenging the basic assumptions of these models when ...

In this thesis we consider a number of enumerative combinatorial problems. We solve the problems of enumerating Eulerian orientations by edges and quartic Eulerian orientations counted by vertices. We also find and prove ...

Fluid flows at micro- and nanometre length scales are governed by physical processes that are quite different to their macroscale counterparts. When these flows interact with suspended solid particles, a rich array of ...

This thesis focuses on the problem of determining the isoperimetric numbers of Levi graphs of balanced incomplete block designs. We study two versions of this: the vertex-isoperimetric number and the edge-isoperimetric ...

Lightning-caused wildfire is a significant concern for fire management agencies worldwide. Unlike other ignition sources, lightning fires often occur in remote and inaccessible locations making detection and suppression ...

Nanoengineering has recently emerged as a promising technology for the understanding, treatment, and diagnosis of disease. One of its most compelling potential uses is in the design of particles with controlled interactions ...

For a multivariate random walk with i.i.d. jumps satisfying the Cramer moment condition and having a mean vector with at least one negative component, we derive the exact asymptotics of the probability of ever hitting the ...

This thesis explores the possible use of Schubert cells, Schubert varieties and flag varieties in finite geometry, particularly in regard to the question of these objects might be a source of understanding of ovoids or ...